Effect of self-deflection on a totally asymmetric simple exclusion process with functions of site-assignments

This study proposes a model of a totally asymmetric simple exclusion process on a single channel lane with functions of site-assignments along the pitlane. The system model attempts to insert a new particle to the leftmost site at a certain probability by randomly selecting one of the empty sites in the pitlane, and reserving it for the particle. Thereafter, the particle is directed to stop at the site only once during its travel. Recently, the system was determined to show a self-deflection effect, in which the site usage distribution biases spontaneously toward the leftmost site, and the throughput becomes maximum when the site usage distribution is slightly biased to the rightmost site, instead of being an exact uniform distribution. Our exact analysis describes this deflection effect and show a good agreement with simulations.